On a structure of the fixed point set of homogeneous maps

Previous Article
Pointwise estimates for solutions of singular quasi-linear parabolic equations
DCDS-S Home
This Issue
Next Article
Unbounded sequences of cycles in general autonomous equations with periodic nonlinearities

August 2013, 6(4): 1017-1027. doi: 10.3934/dcdss.2013.6.1017

On a structure of the fixed point set of homogeneous maps

Yakov Krasnov ^1,2,3, , Alexander Kononovich ^1,2,3, and Grigory Osharovich ^1,2,3,

1.	Department of Mathematics
2.	Bar-Ilan University
3.	Ramat-Gan, 52900

Received June 2011 Revised September 2011 Published December 2012

Abstract
Related Papers

A spectral and inverse spectral problem for homogeneous polynomial maps is discussed.The $m$-independence of vectors based on the symmetric tensor powers performs as a main toolto study the structure of the spectrum. Possible restrictions on this structureare described in terms of syzygies provided by the Euler-Jacobi formula.Applications to projective dynamics are discussed.

Keywords: Fixed points theory, Bzout theorem, Euler-Jacobi formula, multi-linear analysis, syzygies..

Mathematics Subject Classification: Primary: 34A34, 15A69; Secondary: 15A18, 34C14, 34C4.

Citation: Yakov Krasnov, Alexander Kononovich, Grigory Osharovich. On a structure of the fixed point set of homogeneous maps. Discrete and Continuous Dynamical Systems - S, 2013, 6 (4) : 1017-1027. doi: 10.3934/dcdss.2013.6.1017

References:

[1]	Bull. London Math. Soc., 13 (1981), 412-414. doi: 10.1112/blms/13.5.412.
[2]	Ann. of Math. (2), 88 (1968), 451-491.
[3]	Comm. Algebra, 31 (2003), 4571-4609. doi: 10.1081/AGB-120022810.
[4]	"Proc. Edinburgh Math. Soc." (2), 55, Issue 3, (2012), 577-589.
[5]	Berlin, New York: Springer-Verlag, 1974.
[6]	Bull. London Math. Soc., 36 (2004), 378-382. doi: 10.1112/S0024609303002820.
[7]	Second edition, in "Ergebnisse der Mathematik und ihrer Grenzgebiete," Springer-Verlag, 2 1998. doi: 10.1007/978-1-4612-1700-8.
[8]	Acta Sci. Math. (Szeged), 39 (1977), 341-351.
[9]	J. Dyn. Diff. Equat., 21 (2009), 487-499. doi: 10.1007/s10884-009-9141-x.
[10]	Berlin, New York: Springer-Verlag, Band 213, 1974.
[11]	J. Amer. Math. Soc., 6 (1993), 459-501. doi: 10.2307/2152805.
[12]	Topological Methods in Nonlinear Analysis, 19 (2002), 257-273.
[13]	Ann. Math., 66 (1957), 545-556.
[14]	Bull. London Math. Soc., 11 (1979), 177-183. doi: 10.1112/blms/11.2.177.

show all references

References:

[1]	Bull. London Math. Soc., 13 (1981), 412-414. doi: 10.1112/blms/13.5.412.
[2]	Ann. of Math. (2), 88 (1968), 451-491.
[3]	Comm. Algebra, 31 (2003), 4571-4609. doi: 10.1081/AGB-120022810.
[4]	"Proc. Edinburgh Math. Soc." (2), 55, Issue 3, (2012), 577-589.
[5]	Berlin, New York: Springer-Verlag, 1974.
[6]	Bull. London Math. Soc., 36 (2004), 378-382. doi: 10.1112/S0024609303002820.
[7]	Second edition, in "Ergebnisse der Mathematik und ihrer Grenzgebiete," Springer-Verlag, 2 1998. doi: 10.1007/978-1-4612-1700-8.
[8]	Acta Sci. Math. (Szeged), 39 (1977), 341-351.
[9]	J. Dyn. Diff. Equat., 21 (2009), 487-499. doi: 10.1007/s10884-009-9141-x.
[10]	Berlin, New York: Springer-Verlag, Band 213, 1974.
[11]	J. Amer. Math. Soc., 6 (1993), 459-501. doi: 10.2307/2152805.
[12]	Topological Methods in Nonlinear Analysis, 19 (2002), 257-273.
[13]	Ann. Math., 66 (1957), 545-556.
[14]	Bull. London Math. Soc., 11 (1979), 177-183. doi: 10.1112/blms/11.2.177.

[1]	Liang Huang, Jiao Chen. The boundedness of multi-linear and multi-parameter pseudo-differential operators. Communications on Pure and Applied Analysis, 2021, 20 (2) : 801-815. doi: 10.3934/cpaa.2020291
[2]	JIAO CHEN, WEI DAI, GUOZHEN LU. $L^p$ boundedness for maximal functions associated with multi-linear pseudo-differential operators. Communications on Pure and Applied Analysis, 2017, 16 (3) : 883-898. doi: 10.3934/cpaa.2017042
[3]	Paula Kemp. Fixed points and complete lattices. Conference Publications, 2007, 2007 (Special) : 568-572. doi: 10.3934/proc.2007.2007.568
[4]	John Franks, Michael Handel, Kamlesh Parwani. Fixed points of Abelian actions. Journal of Modern Dynamics, 2007, 1 (3) : 443-464. doi: 10.3934/jmd.2007.1.443
[5]	Byung-Soo Lee. A convergence theorem of common fixed points of a countably infinite family of asymptotically quasi-$f_i$-expansive mappings in convex metric spaces. Numerical Algebra, Control and Optimization, 2013, 3 (3) : 557-565. doi: 10.3934/naco.2013.3.557
[6]	Alexey A. Petrov, Sergei Yu. Pilyugin. Shadowing near nonhyperbolic fixed points. Discrete and Continuous Dynamical Systems, 2014, 34 (9) : 3761-3772. doi: 10.3934/dcds.2014.34.3761
[7]	Zhihong Xia, Peizheng Yu. A fixed point theorem for twist maps. Discrete and Continuous Dynamical Systems, 2022, 42 (8) : 4051-4059. doi: 10.3934/dcds.2022045
[8]	Jacek Banasiak, Aleksandra Puchalska. Generalized network transport and Euler-Hille formula. Discrete and Continuous Dynamical Systems - B, 2018, 23 (5) : 1873-1893. doi: 10.3934/dcdsb.2018185
[9]	José Natário. An elementary derivation of the Montgomery phase formula for the Euler top. Journal of Geometric Mechanics, 2010, 2 (1) : 113-118. doi: 10.3934/jgm.2010.2.113
[10]	Behrouz Kheirfam, Kamal mirnia. Multi-parametric sensitivity analysis in piecewise linear fractional programming. Journal of Industrial and Management Optimization, 2008, 4 (2) : 343-351. doi: 10.3934/jimo.2008.4.343
[11]	Juan Campos, Rafael Ortega. Location of fixed points and periodic solutions in the plane. Discrete and Continuous Dynamical Systems - B, 2008, 9 (3&4, May) : 517-523. doi: 10.3934/dcdsb.2008.9.517
[12]	Fabian Ziltener. Note on coisotropic Floer homology and leafwise fixed points. Electronic Research Archive, 2021, 29 (4) : 2553-2560. doi: 10.3934/era.2021001
[13]	Francisco Crespo, Sebastián Ferrer. On the extended Euler system and the Jacobi and Weierstrass elliptic functions. Journal of Geometric Mechanics, 2015, 7 (2) : 151-168. doi: 10.3934/jgm.2015.7.151
[14]	Yeping Li. Existence and some limit analysis of stationary solutions for a multi-dimensional bipolar Euler-Poisson system. Discrete and Continuous Dynamical Systems - B, 2011, 16 (1) : 345-360. doi: 10.3934/dcdsb.2011.16.345
[15]	David McCaffrey. A representational formula for variational solutions to Hamilton-Jacobi equations. Communications on Pure and Applied Analysis, 2012, 11 (3) : 1205-1215. doi: 10.3934/cpaa.2012.11.1205
[16]	Shui-Hung Hou. On an application of fixed point theorem to nonlinear inclusions. Conference Publications, 2011, 2011 (Special) : 692-697. doi: 10.3934/proc.2011.2011.692
[17]	Manuel de León, David Martín de Diego, Miguel Vaquero. A Hamilton-Jacobi theory on Poisson manifolds. Journal of Geometric Mechanics, 2014, 6 (1) : 121-140. doi: 10.3934/jgm.2014.6.121
[18]	Piotr Fijałkowski. A global inversion theorem for functions with singular points. Discrete and Continuous Dynamical Systems - B, 2018, 23 (1) : 173-180. doi: 10.3934/dcdsb.2018011
[19]	Victoria Martín-Márquez, Simeon Reich, Shoham Sabach. Iterative methods for approximating fixed points of Bregman nonexpansive operators. Discrete and Continuous Dynamical Systems - S, 2013, 6 (4) : 1043-1063. doi: 10.3934/dcdss.2013.6.1043
[20]	Rich Stankewitz. Density of repelling fixed points in the Julia set of a rational or entire semigroup, II. Discrete and Continuous Dynamical Systems, 2012, 32 (7) : 2583-2589. doi: 10.3934/dcds.2012.32.2583

2020 Impact Factor: 2.425

Tools

Metrics

Other articles
by authors

on AIMS
Yakov Krasnov Alexander Kononovich Grigory Osharovich
on Google Scholar
Yakov Krasnov Alexander Kononovich Grigory Osharovich

[Back to Top]